周期情形下水波系统解映射的不一致连续性

Non-uniform Continuity of Solution Mapping of Water Wave System in Periodic Case

基于解的局部适定性,利用近似解方法讨论周期情形下一个两分量水波系统Cauchy问题解在Besov空间B,(T)×B,(T)中对初值的不一致连续依赖性.结果表明,该问题的解在对应Besov空间中的局部适定性不能只依赖压缩映像原理得到.

Based on the local well-posedness of the solution,we discussed the non-uniformly continuous dependence of the solutions to the Cauchy problem associated with the periodic water wave system on initial value in Besov spaces B,(T)×B,(T)by using the method of approximate solutions.The results show that the local well-posedness of the solutions to this problem in the corresponding Besov spaces can not be obtained only by contraction mapping principle.